As the U.S. oil-and-gas boom rolls into its second decade, a new idea is starting to resonate with regulators and communities: Certain places should simply be off-limits to drilling.

That is not how it has worked up until now. Over the past decade, oil and gas wells have been drilled for hydraulic fracturing in suburban subdivisions, airports, public parks and golf courses. As long as energy companies leased the mineral rights, they...